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Cooling of heat-generating elements in different engineering fields is a very important and crucial topic. The present research is devoted to numerical analysis of thermogravitational convection of a pseudoplastic nanosuspension in a chamber with two heated bottom wall sections of various heat fluxes and isothermally cooling vertical walls. A mathematical model formulated employing the time-dependent Oberbeck–Boussinesq equations with non-primitive variables has been worked out by the finite difference technique. It has been revealed that a mixture of 1% carboxymethylcellulose with water can be the most effective medium to cool the heat-generating elements. At the same time, aluminum oxide nano-sized solid particles have a more essential cooling impact on the heated sections.